I think that this approach is basically a "sink or swim" situation. As a teacher in the public sphere, I think about what I would have to teach so that students would be capable of solving, or even engaging in a solution of these problems. The Exeter situation seems to assume that their students come to them WITH the skills, which are then honed through solving these problems. Either that or those who can't solve them fail out - at Exeter that the way it goes. But at public schools, we don't have that luxury, we need to teach these skills rather than only identify the students who either already know them, or acquire them independently. Now, this is not to say that the teachers at Exeter aren't teaching, but I believe that it is a very different environment than what we face in the public sphere.
It reminds me of the Juku system in Japan where the skills and practice are handled by the private cram schools while the public schools simply assume that everybody (who is anybody) will be paying for the Juku and thus the public schools focus almost exclusively on conceptual problem solving.
The Japanese style problems are here:
Again, I would hesitate to call these reform problems because they require so much real mathematical knowledge.
An interesting comment of the juku phenomenon is here: